Drawing a nurbs curve along a surface
I would just use Snapping.


set Snapping to Face
grab a curve point while holding Ctrl to temporarily enable the Snap to follow the shape of a target object




You can also take a look at Shrinkwrap modifier, but it can be little tricky for this kind of usage.
https://docs.blender.org/manual/en/latest/modeling/modifiers/deform/shrinkwrap.html